# Exact observability of a 1D wave equation on a non-cylindrical domain

## TL;DR

This paper investigates the conditions under which a one-dimensional wave equation on a time-dependent domain can be exactly observed from boundary and interior points, including moving observers, with implications for control and monitoring.

## Contribution

It provides new criteria for exact observability and admissibility of wave equations on non-cylindrical domains, extending previous results to moving observers and interior observations.

## Key findings

- Established observability estimates for boundary and interior observations.
- Extended observability results to moving observers within the domain.
- Provided conditions for admissibility of boundary observation.

## Abstract

We discuss admissibility and exact observability estimates of boundary observation and interior point observation of a one-dimensional wave equation on a time dependent domain for sufficiently regular boundary functions. We also discuss moving observers inside the non-cylindrical domain and simultaneous observability results.